I've been keeping physical statements for most of my cards (most are only months old). If you have over a dozen cards and you need to look them up come tax season then it's a lot easier to already have physical statements.
Keep in mind that with some banks if you cancel a card it becomes harder to request statements.
Chase requires you to fax in a bunch of details to a special office. I've been meaning to do this for one of my cards but I've already forgotten what to send and where to send it.